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## IMC 2013 Problem 4

Problem 4. Let ${n \geq 3}$ and let ${x_1,..,x_n}$ be nonnegative real numbers. Define ${A=\sum\limits_{i=1}^n x_i, B = \sum\limits_{i=1}^n x_i^2}$ and ${C= \sum\limits_{i=1}^n x_i^3}$. Prove that

$\displaystyle (n+1)A^2B +(n-2)B^2 \geq A^4+(2n-2)AC.$